Grassmann manifolds have received a lot of recent attention from the
machine learning community, in both classic learning and learning using deep neural network problems. Linear discriminant analysis [1]}, a class of supervised learning algorithms whose goal is to differentiate data on a latent subspace, has been successfully recast as a Grassmannian kernel method [2]}, [3]}. An extension of traditional spectral clustering that attempts to increase the accuracy of the final clustering result by leveraging the sparsity of the matrix describing the connectivity of the graph through regularization terms [4]} has been recently reformulated into a Grasmannian optimization problem [5]}. The nature of the manifold, with its intrinsic structural preserving orthogonality constraints, makes it a suitable alternative for low rank matrix completion, i.e., the problem of filling the missing entries of a given sparse matrix [6]}. In deep learning applications, Grassmann manifolds have
also been used to improve
the performance of algorithms in visual domain adaptation problems [7]} and in the construction of deep neural networks [8]}. A detailed overview of recent advancements in the field is offered in [9]}.
